Some Characterizations of Open, Closed, and Continuous Mappings
We obtain new characterizations of open maps in terms of closures, of closed maps in terms of interiors, and of continuous maps in terms of interiors. Further open (closed) onto maps 𝑓∶𝑋→𝑌 are described in terms of images under 𝑓 of certain closed (open) sets in 𝑋. Continuity of (onto) maps is also...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2008-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/527106 |
| id |
doaj-612fafed53ab4c0dab77da8a3cd92a92 |
|---|---|
| record_format |
Article |
| spelling |
doaj-612fafed53ab4c0dab77da8a3cd92a922020-11-24T22:32:24ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/527106527106Some Characterizations of Open, Closed, and Continuous MappingsNavpreet Singh Noorie0Rajni Bala1Department of Mathematics, Faculty of Physical Sciences, Punjabi University, Patiala 147002, IndiaDepartment of Mathematics, Faculty of Physical Sciences, Punjabi University, Patiala 147002, IndiaWe obtain new characterizations of open maps in terms of closures, of closed maps in terms of interiors, and of continuous maps in terms of interiors. Further open (closed) onto maps 𝑓∶𝑋→𝑌 are described in terms of images under 𝑓 of certain closed (open) sets in 𝑋. Continuity of (onto) maps is also characterized in terms of saturated sets.http://dx.doi.org/10.1155/2008/527106 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Navpreet Singh Noorie Rajni Bala |
| spellingShingle |
Navpreet Singh Noorie Rajni Bala Some Characterizations of Open, Closed, and Continuous Mappings International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Navpreet Singh Noorie Rajni Bala |
| author_sort |
Navpreet Singh Noorie |
| title |
Some Characterizations of Open, Closed, and Continuous Mappings |
| title_short |
Some Characterizations of Open, Closed, and Continuous Mappings |
| title_full |
Some Characterizations of Open, Closed, and Continuous Mappings |
| title_fullStr |
Some Characterizations of Open, Closed, and Continuous Mappings |
| title_full_unstemmed |
Some Characterizations of Open, Closed, and Continuous Mappings |
| title_sort |
some characterizations of open, closed, and continuous mappings |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2008-01-01 |
| description |
We obtain new characterizations of open maps in terms of closures, of closed maps in terms of interiors, and of continuous maps in terms of interiors. Further open (closed) onto maps
𝑓∶𝑋→𝑌 are described in terms of images under 𝑓 of certain closed (open) sets in 𝑋. Continuity of (onto) maps is also characterized in terms of saturated sets. |
| url |
http://dx.doi.org/10.1155/2008/527106 |
| work_keys_str_mv |
AT navpreetsinghnoorie somecharacterizationsofopenclosedandcontinuousmappings AT rajnibala somecharacterizationsofopenclosedandcontinuousmappings |
| _version_ |
1725734065245519872 |